This invention relates to a digital write-and-read method and an apparatus thereof. More specifically, it relates to a write-and-read method of digital signals which will be suitable for magnetic disk systems for writing digital data in a high density, a signal processing method and an apparatus applying the method.
Recently, requirements for high density recording and high speed operation have become eager for magnetic recording media, particularly those having a diameter of not greater than 3.5 inches. One of the reasons is that large capacity storage systems have mainly shifted to a RAID (Redundant Arrays of Inexpensive Disks) systems and performance of high-end small magnetic disks directly affect system performance.
On the other hand, large scale softwares taking a human interface into consideration such as a GUI (Graphical User Interface) have become inevitably necessary for personal computers as the principal application of small magnetic disks, and the target of a disk capacity in 1995,for example, is said to be about 1 G byte in the case of 2.5-in disk systems.
To satisfy such requirements, two to three 2.5-in disks (recording on four to six surfaces) are necessary in the maximum recording density (800M bit/in..sup.2) at the present product level. To attain such a recording density on one disk (two surfaces), high density recording of about 1.5 G bit/in..sup.2 is necessary.
The operation speed of the personal computers has almost reached 300 MIPS (Million computer Instructions Per Second) in 1995, and a higher operation speed of the small magnetic disk has been required, as well. The write-and-read speed inside the present high-end magnetic disks is 80 to 120M bit/sec.
To support such a progress of the magnetic disks, signal processing technique of the write-and-read systems, too, has made progress to cope with high density recording and high speed recording. As to channel codes, for example, a channel code having a code rate of 8/9 has become predominant from a run-length limited code having a code rate of 2/3. On the other hand, because the length between the adjacent recording bits has become smaller so as to attain high density recording, interference between the signals for each bit has become greater, the specification of the signal-to-noise ratio necessary for playing back and detecting the original recording signals has become higher by a peak-detection method according to the prior art. Therefore, PR4ML (Partial Response class 4 with Maximum Likelihood decoding) system which employs partial response equalization which takes inter-symbol interference into consideration and which can detect maximum likely signal strings from the playback signals has been examined. An LSI for this system has been developed already and are being packaged to products. One of the prior art references associated with this system is U.S. Pat. No. 5,497,384.
In a write-and-read system with greater inter-symbol interference, the equalization method of the partial response must be changed from PR4 to EPR4 (Extended PR4), and along with this change, an ML (Maximum Likelihood decoding) circuit must be made more complexed from the 2-state to the 8-state. In this case, the number of the states may be interpreted as the number of candidates necessary for finding out the most likely signals. The application of the EPR4ML circuit to the magnetic disks is described, for example, in JP-A-7249998.
In high density recording by increasing a track density, on the other hand, the signal-to-noise ratio of the write-and-read system drops. To overcome this drop has become a critical problem. One of the methods for solving this problem is the utilization of trellis codes. Since the ML circuit executes digital processings, its LSI configuration can be attained relatively easily. Therefore, trellis codes can cope with a low signal-to-noise ratio by providing those characteristics which are suitable for the ML processing to the channel codes themselves on the premise of the use of a complicated ML processing.
Since the ML processing deals with the transition state of the codes, that is, a trellis diagram, the channel codes premised on the ML processing are referred to as the "trellis codes". The study of this processing was started in the mid of '80 by researchers of a communication theory and in order to establish a practical channel coding technology, matching with a playback equalization system, limit of the number of continuation of the same codes, counter-measures for error propagation, the removal of DC components, and so forth, have been examined.
For example, "IEEE Transactions on Information Theory", Vol. 37, No. 3, pp. 818-855, 1991 reports a theoretical study of the trellis codes called "MSN (Matched Spectral Null) codes" characterized by the DC-free code, and represents that a bi-phase MSN code having a code rate of 1/2 can be applied to EPR4 equalization. The term "bi-phase code" represents the system which generates a recording signal (C') by causing "10" or "01" to correspond as the channel code (C) to "1" of a data bit (D) and "11" or "00" to "0" of the data bit (D) as shown in FIG. 21 of the accompanying drawings.
Further, "IEEE Transactions on Magnetics", Vol. 31, No. 2, pp. 1208-1213, 1995 reports a tentative production of an LSI for the MSN codes having a code rate of 8/10 on the assumption of PR4 equalization.
To accomplish a large improvement of the signal-to-noise ratio by ML decoding, an Euclidean distance in an equalization output code string of the channel codes must be increased. The square of the Euclidean distance, i.e. dE.sup.2, is defined by the following formula between two code strings "u=u.sub.1, u.sub.2, . . . , u.sub.n " and "v=v.sub.1, v.sub.2, . . . , v.sub.n " the with length n. ##EQU1##
The received signal is the sum of the original correct decoded value and the noise. When the channel code group having a large dE value is selected in the original equalization output series free from the noise, the influences of the noise on the received signal become weak and the maximum likely codes can be decoded more easily.
One of the methods for holding dE is a so-called "set partition method", which uses a plurality of sets of channel codes holding dE in the equalization output series. FIG. 22 shows an example of this set partition.
In this example, the input data bit D is divided into every 2 bits, and the channel code C is allocated to four kinds of bit patterns ranging from "00" to "11". Each channel code is magnetically recorded on a magnetic disk through a magnetic head and receives PR(1, -1) equalization at the time of playback. The anticipated output by this equalization is represented by symbol E in FIG. 22. In this example, the data D is represented by the sets of two bit patterns, the second bit of which is different.
The channel codes "00" and "10" are allocated to the set of "00" and "01", for example. When the channel codes "00" and "01" are played back, the PR(1, -1) equalization outputs are given by "0, 0" and "2, -2" and the Euclidean distance dE.sup.2 is given by "2.sup.2 + (-2).sup.2 =8".
FIG. 23 shows the case where the PR (1, -1) equalization output become "2, -2" when the state of the previous channel code is "*0" (where symbol * means that it may be either 0 or 1) and is represented as the state so.
In PR(1, -1) equalization, equalization is so made as to provide a response expressed by "1, -1" to the channel code "1" in consideration of the inter-symbol interference. In other words, this equalization assumes the inter-symbol interference of one other bit in addition to the bit output. The equalization system with little noise emphasis and suitable for magnetic recording can be thus obtained by employing the response system which takes the inter-symbol interference suitable for magnetic recording into consideration. When the channel code is "0", a "-1, 1" response is obtained by the inversion output of "1". The sum of the PR(1, -1) equalization output of each channel code is the equalization output. The output of the channel code as shown in FIG. 23 is "2, -2". The expected outputs can be calculated similarly for other channel codes, and the Euclidean distance can be determined from the difference of the expected equalization outputs of the two channel codes. When the combination of the set partition by PR(1, -1) equalization is considered in this way, its Euclidean distance dE.sup.2 is "8".
Similarly, if a set partition having a large Euclidean distance and suitable for EPR4 can be constituted and the trellis codes can be constituted by using the channel code group, channel codes more resistant to the noise than in the prior art system can be constituted. Because EPR4 is the system which takes the 3-bit inter-symbol interference into consideration for the channel codes, however, selection of the channel codes depends not only the input data bit D but also on the previous channel code C. No proposal has yet been made on the construction of the set-partition for EPR4 which takes these points into consideration.
Since the conventional trellis code suitable for EPR4 equalization is based on the bi-phase code, etc., it has a low code rate, whereas the trellis code having a high code rate is not the system suitable for EPR4 equalization.